The path integral formalism applied to photon migration in turbid media

Abstract

The propagation of light in a multiply scattering (turbid) medium is of importance in many fields, most recently in medicine with the advent of photodynamic therapy (PDT) and near infra-red (NIX) tissue spectroscopic and imaging methods. The distribution of photon trajectories in highly scattering media is usually estimated by random sampling i.e. Monte Carlo methods. The Path Integral (PI) formalism represents an alternative approach: instead of finding the most likely paths by random sampling, PI is used to identify them directly. This work describes a novel reformulation of the PI method using a local coordinate system approach conventional in differential geometry. This allows explicit inclusion of absorption coefficients and, unlike previous PI formulations, is not limited to computation of 'non-absorption' paths. The method has been used to calculate the small scale distribution of light in a simple backscattering geometry. The PI prediction is significantly at variance with that of the diffusion approximation and experimental results are presented that support the PI picture.